How do you change #a^(1/2)b^(4/3)c^(3/4)# into radical form?

Question

Hazel Anglin · Accepted Answer

See a solution process below:

First, we can use this rule of exponents to put the #a# term into radical form: #x^(1/color(red)(n)) = root(color(red)(n))(x)# #a^(1/color(red)(2))b^(4/3)c^(3/4) => (root(color(red)(2))(a))b^(4/3)c^(3/4) => (sqrt(a))b^(4/3)c^(3/4)# Next, we can use this rule of exponents to rewrite the #b# and #c# terms: #x^(color(red)(a) xx color(blue)(b)) = (x^color(red)(a))^color(blue)(b)# #(sqrt(a))b^(4/3)c^(3/4) => (sqrt(a))b^(color(red)(4) xx color(blue0)(1/3))c^(color(red)(3) xx color(blue)(1/4)) => sqrt(a)(b^4)^(1/3)(c^3)^(1/4)# We can again use this rule of exponents to put the #b# and #c# terms in radical form: #x^(1/color(red)(n)) = root(color(red)(n))(x)# #sqrt(a)(b^4)^(1/color(red)(3))(c^3)^(1/color(red)(4)) => sqrt(a)root(color(red)(3))(b^4)root(color(red)(4))(c^3)#

Ethan Adkins · Answer

undefined To change $a^{\frac{1}{2}}b^{\frac{4}{3}}c^{\frac{3}{4}}$ into radical form, you would rewrite each exponent as a radical:

$a^{\frac{1}{2}}$ becomes $\sqrt{a}$

$b^{\frac{4}{3}}$ becomes $\sqrt[3]{b^4}$

$c^{\frac{3}{4}}$ becomes $\sqrt[4]{c^3}$

So, the expression in radical form would be $\sqrt{a} \times \sqrt[3]{b^4} \times \sqrt[4]{c^3}$.